curve #356

y² = x³ + x² − 24391876744717707263532695900840552395172973498186560300x + 46943906433780620456844832699051340439698711588743845207309557656274241785479710000

a-invariants: [0, 1, 0, -24391876744717707263532695900840552395172973498186560300, 46943906433780620456844832699051340439698711588743845207309557656274241785479710000]
rank (lower bound): ≥ 29
torsion subgroup: trivial
conductor (N): 1138311211986944120854212482517370029218279069247307312958252982216018500197158165165915709784372000548257520927912312147452126835606642920
naive height: 394.2398 ★ record for rank ≥ 29
Faltings height: 30.7273 ★ record for rank ≥ 29
discriminant (Δ): -23225588805821255971980452316400390985539123780447843034585631625599190483310342757460742687943805554853363674964538200142891911461727552231886578226014220310540000000 ★ record for rank ≥ 29
primes of bad reduction: 2, 3, 5, 13, 23, 29, 37, 41, 139, 751, 28960331, 1204882855601765528877267647500895974865482613, 197980272243427555346397293722916980361535459279712115031762027678304939
regulator: 179522411193788517037233594749787079.516976892843255294998754048012465830001259791480551298327742
submitted by: wgxli
submitted at: 2026-08-25 14:20:06 UTC
last updated: 2026-08-25 14:20:06 UTC

Witness: 29 independent points

(-326997921211503588229214581626427744550107296985130/118586039247125879193769, 12469367393431087472272749661661489940471014953584266372757122302525155874590/40836672381196042952343937217591147)
(882384672297002231135604329050, -828858022193514373698121603106394253283827650)
(244763365296360444948448278334/25, -108007657315858188020341319638683534867279402/125)
(-1276392432978390427723666850, -275677426209369608514674875796018815109250)
(15384289084600063252342766606230/5041, 10901792198960027560548341454797417559021575130/357911)
(44169116725816001340178662656614549270/45606592249, -1516042022968746289196607492433064866683193756583581909710/9739607020919693)
(60971270338557873265265382510908119438600/2425036906009, 14784585322654888497456025709159994143519254148310312178540500/3776395996993233277)
(15896696350479699754319254762/9, -2613715903370034669065266303121268861459382/27)
(2769556317106639959947310135484480656176671675/46562149020065449, 145265273634242392146615567077705550642163008135572174583366234404100/10047303579309582618201707)
(-16363275482474806375730825983840040230550/6248665071289, -4759893868701009595924826331041900904353635732761406282114950/15619994284648465837)
(105074584691050246593459590614/25, -17080346312754784813794394935397962873730962/125)
(-118457702896365108531517391122549777388600/34522217064721, -60932208415442710438448498274240968475437513481182138694370500/202837392219009183481)
(-1084690449748472954875613188845890/461041, -94594034290535932399897646418562641325679171377710/313046839)
(-203213504328188656596754401082876968390444221/415396956896987521, -64898355601797396227048002436739212670282477309594829352926254248940/267728722680066799139759681)
(-3464706420735358275063613337, 299772584170404560075266311074307509880054)
(624208166229108198559186440202/49, 460630098018014154524930436943428839976289698/343)
(4144928193283308751061595197010/1681, -2916912030052513323045386734850731220124687690/68921)
(423037345432857402307659179514568145793651031893955495/7858867914426199468741441, -274030109416605784013285959059779024755345691177067493264119141908966014183298070/22031292899812985270122856486212555489)
(5522412748030341068060999778415198492618/1669499152281, -106840855459063356417470530538750477542808766937543666336826/2157144829169909571)
(1149651334807678436735364898840586399051787166/289592469374341225, -17546096826504248933219281619627382567816364460453092935041983394586/155840702148432810037107125)
(1518417215908235031323748352644765919881397/333744742017124, -1058567848755074924376559065743390766895458666411640508760558633/6097076561082876910568)
(41332857202888814162780100909662315777562559998154/10239854947720186264921, -123708496650397002168637321362669795161565876122325195556993512306664902150/1036193126373912689024174893610531)
(404676329752131470000300780645743356679/115437537121, -2635916885456672090069880848974352968106545604038214415210/39221173049768081)
(406476792522832378325166730986887675756389091222094030/36756788885116691329110481, 236844515350966520183344722237458239719970993898304554803152363310826912988216030/222846771117705654953031952006169700121)
(958179770121347392935365441432732746318316530555/83558610032904175129, 862506579876825007801548847336289484456063267643489417385020088758869240/763812586377469346973980619133)
(30494161469403277987072261505693992667350/722199131329, 5290185907026110024733751620416034694619615659544312722142250/613741432383404767)
(650635614129389500251944174620286728977147037409397540850/2787503142830154964064065969, 16592441994964905663211327186665679285172978898083092583823779065931697886982716010250/147171273718078941821388198446460831640297)
(3888374259935916765161676350390548187360650/1009198263230161, 3231683579484592785979651199861584661352775648476033711494957250/32060090331702430258841)
(423061327161750793830176375225821270265119008070/2056971785617084249, 275093870895611513619263446813311149216641192371022559332374577658552610/2950139158018468301734670557)

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